Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l }
16 x ^ { 2 } + 2 y ^ { 2 } & = 70 \
y ^ { 2 } - 16 x ^ { 2 } & = 38
\end{array} \right)$$
A) $\left( \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( - \frac { i \sqrt { 2 } } { 4 } , - 6 \right)$
B) $\left( - \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( \frac { i \sqrt { 2 } } { 4 } , - 6 \right)$
C) $\left( \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( - \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( \frac { i \sqrt { 2 } } { 4 } , - 6 \right) , \left( - \frac { i \sqrt { 2 } } { 4 } , - 6 \right)$

Question

Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l } 
16 x ^ { 2 } + 2 y ^ { 2 } & = 70 \
y ^ { 2 } - 16 x ^ { 2 } & = 38
\end{array} \right)$$
A) $\left( \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( - \frac { i \sqrt { 2 } } { 4 } , - 6 \right)$
B) $\left( - \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( \frac { i \sqrt { 2 } } { 4 } , - 6 \right)$
C) $\left( \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( - \frac { i \sqrt { 2 } } { 4 } , 6 \right) , \left( \frac { i \sqrt { 2 } } { 4 } , - 6 \right) , \left( - \frac { i \sqrt { 2 } } { 4 } , - 6 \right)$

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, resulting in $32x^2 = 108$, which simplifies to $x^2 = \frac{27}{8}$. Solving for $x$ gives $x = \pm \frac{i\sqrt{2}}{4}$. Substituting $x$ back into one of the original equations allows solving for $y$, resulting in $y = \pm 6$. Thus, there are four possible combinations of $x$ and $y$, as listed in option C.

Solve the System by the Substitution or Elimination Method (16x2+2y2=70y2−16x2=38)\left( \begin{array} { r l } 16 x ^ { 2 } + 2 y ^ { 2 } & = 70 \\y ^ { 2 } - 16 x ^ { 2 } & = 38\end{array} \right)(16x2+2y2y2−16x2​=70=38​)

Solve the System by the Substitution or Elimination Method $\left( \begin{array} { r l } 16 x ^ { 2 } + 2 y ^ { 2 } & = 70 \\y ^ { 2 } - 16 x ^ { 2 } & = 38\end{array} \right)$